Current Proceedings on Technology
Yazarlar: Zhanar Omarova, Meyirha Bektegenov
Konular:-
Anahtar Kelimeler:Fictitious domain method,Convergence,Alternating direction method,Over relaxation method,Lowconcentratesolution,Concentration distributions
Özet: There is considered a mathematical model of a low-concentrated salt solution movement in a closed curvilinearfield. We have to take into account the inflow solution through the boundary, the presence of evaporation ofwater from the surface of the reservoir, precipitation of salts in those points, where the concentration of thesated solution is reached. On a part of the area boundary where the solid walls are assumed as boundaryconditions for a velocity are accepted the conditions of sticking, for concentration is accepted the condition ofnot flow out. On a part of the boundary, where the liquid flows into the considered area, both components ofthe velocity and the concentration are given. We assume that we have several sources inflowing in theconsidered area.The purpose of the study is to develop an algorithm for numerical solution of the mathematical model and toconduct a computational experiment for determining of consistent patterns of concentration distribution in theselected area provided the balance of evaporation and precipitation of salts exists.The equations are considered for curvilinear area , simulating outlines of some reservoir, in natural variablesu, , P . Therefore for researching of the given problem is offered to use the fictitious domain method withprolongation by lower-order coefficients. The problem is considered on a complicated domainD, strictlycontaining area ( D) , with the boundary 1 S . For the numerical solution of the problem are used the alternating direction method, obvious scheme of decomposition on the physical factors and over relaxationmethod.The obtained graphs of vector's fields and concentration distributions characterize circulation of a salt solution inthe selected area. Provided balance of evaporation and precipitation of salt in a part of area remote from asource, is accumulated a salt solution of the greater concentration, while in a part of area near to a source, thelow-concentrate solution is saved. If reduce we observe the good convergence of the numerical algorithm.